Question

Force acting on a body varies with time as shown below. If initial momentum of the body is $\vec{p}$, then the time taken by the body to retain its momentum $\vec{p}$ again is

• A. 8 s
• B. $(4+2 \sqrt{2}) s$
• C. 6 s
• D. Can never obtain

Answer 1

Answer: (B)

$\tan \theta=\frac{1}{2}=\frac{F_{0}}{t_{0}-4}$
$\Rightarrow F_{0}=\frac{t_{0}-4}{2}$
Total change in momentum should be zero, then only it will retain its initial momentum.
So, positive area of $F-t$ curve should be equal to negative area of $F-t$ curve till time $t_{0}$.
$\frac{1}{2}(4)(1) =\frac{1}{2}\left(t_{0}-4\right) F_{0}$
$8=\frac{\left(t_{0}-4\right)}{2} \cdot \frac{\left(t_{0}-4\right)}{2}$
$\left(t_{0}-4\right)^{2} =32$
$t_{0} =4+2 \sqrt{2}$